Epitome Astronomiae Copernicanae: Liber III, part 7
Part IV. Of the times of the year and the quantities of the zones
How many parts of the turning year are there, natural times or seasons? Four: spring, summer, autumn, winter. Although some of the ancient historians use only two, summer and winter.
Whence are they so named? Aestas (summer), in Greek theros, both words are derived from heat (aestus), because that part of the year is hot; the German name is taken from the presence of the Sun.
Hiems (winter) is named from rain, because in Greek hyein is to rain, since the sky for the most part holds that part of the year overcast, especially in Italy; in Greek cheimon is a stormy state of the air, for they will have the word derived from the pouring out of rains. In German the name comes from copious winds. Ver (spring), in Greek ear, whence the Latin ver, seems derived from the Hebrew or Syriac word Eijar, which in the Jewish year is the second of the spring months. Eijar has kinship with the Hebrew aer, which signifies vapour, whence the Greek aer, the Latin aer. The German is Frühling, the early or fore-year, as it were the morning part of the year. Autumnus has an Etruscan termination; but the kindred word seems to be the Greek autmē, which seems so called from the frequent exhalation of mists. In Greek it is opōra, from opos, perhaps from the juicy fruits of trees: whence also the German Obst, which signifies tree fruits. The German name seems to descend from laying waste; whence verheeren, to ravage, and Herbst, the cluster of grapes remaining when the leaves have fallen.
By what qualities are these seasons of the year distinguished from one another? Summer is hot, winter cold, the other seasons hold the mean.
Perhaps, then, the length of the day in summer will be the cause of the heat, and its shortness of the cold? Although this is among the causes, it is not the full and genuine cause. For days are longer in the cold zones than either in the temperate or in the torrid, yet the heat is greater in the torrid.
What, then, among celestial things is the genuine cause of heat and cold, and so of summer and winter? The approach of the Sun to the zenith at the hours of noon is the cause of summer, and its recession from the zenith at the hours of noon, when it can be nearest of all to the zenith, is the cause of winter.
Whence comes this approach and recession of the Sun? From the obliquity of the ecliptic, under which the Sun is seen to move. For one semicircle of it inclines from the equator toward the north by 23½ degrees, the other is cast down below the equator toward the south by as many degrees. The sum of the two, 47°, makes the variation of the meridian altitudes of the Sun, more than half of a right angle.
Why, however, does the Sun, high and near the zenith, heat more than when low and approaching the horizon? Because the higher it is, the more directly its ray strikes the plane of the Earth, and so the more strongly. When low it illuminates the lands obliquely, and this irradiation, as with blows elsewhere, is made vain and feeble by the slope.
How are the four parts of the year, spring, summer, autumn, winter, described and defined? Spring in the temperate zone is that space of time in which the Sun ascends from the equinox to the solstice; summer, from the solstice to the autumnal equinox; autumn, from that to the other, winter solstice; winter, from the winter solstice to the vernal equinox.
What do you call solstice and what equinox in this place? Above in the second book they were the four cardinal points of the ecliptic themselves; but here solstice signifies the time, or those days of the year, in which the Sun’s declination from the equator seems to stand still; or rather that moment in which the centre of the Sun touches the solstitial points, at which it declines most and thence begins to return to the equator; the equinox, however, is that moment in which the centre of the Sun occupies the equinoctial points, making the preceding day equal to the following night or the contrary. The Greeks name the solstices with the more significant term tropai hēliou, for the turnings of the Sun take place in a moment. They call them also the four centres or points, a word transferred from the points of the sphere to the corresponding times of the year; with the Hebrews they are thecuphae. By the custom of Latin speech the high solstice is understood when solstitium is named; the low is called bruma. The Greeks are wont to say the summer or winter turning.
Summer seems not rightly defined; for if the height of the Sun intensifies the heat, why is not the summer quadrant counted from the middle of Taurus through Cancer to the middle of Leo, so that the greatest altitude of the Sun, and so the greatest heat, should be in its middle, and the ends of the quadrant on either side have equal altitude of the Sun? The celestial causes alone do not make the summer months hot from 12/22 June to 13/23 September, but the slowness of matter here counts for very much. For although the Sun is equally high in the middle of Taurus and in the middle of Leo, the gross body of the Earth begins to be heated only when the Sun is in Taurus. But when the Sun has passed into Leo the heat has already lasted three months, and to an Earth already made hot before a new heat is daily added, and the clinging heats accumulate for some time in the matter. This also is the cause why the day is hotter two hours after noon than at the noon hour itself. Let the judgment be the same of winter. For although the autumnal and winter quadrants are equal in the lowness of the Sun, yet in autumn there is some heat, in winter pure cold, because, the Sun after the equinox departing little by little from our hemisphere, the Earth, retaining something of the heat of summer, needs time to be cooled; but in winter the Earth, already sufficiently chilled and covered with snows and crusts of ice, cannot so easily be laid bare by the rays of the Sun, refreshed and heated, even though the Sun raises itself little by little from the lowest point of the ecliptic through the same degrees of altitude which it had in the autumnal quadrant. Astronomers therefore do rightly in bringing the seasons, named from their qualities, within the termini of the cardinal quadrants, not of the intermediate points.
What is the comparison of the five zones with the four seasons of the year? The torrid corresponds to summer, the frigid to winter, the temperate to spring and autumn.
On what argument does this comparison rest? Because we have said that the cause of heat is the altitude of the Sun, the consummate altitude of the Sun therefore produces consummate heat, when it acts alone, not helped by time. Now in the torrid zone there is the consummate altitude of the Sun; for the zone is defined by the two tropics, within which the Sun in each place every year comes to the very zenith on two noons, since the ecliptic, the Sun’s path, extends from one tropic to the other. Conversely, because we have said that the cause of winter is the lowness of the Sun at the times of noon, the full lowness of the Sun, that is, depression below the horizon and so absence at the time of noon, causes pure cold. Now in the frigid zones, which the polar circle bounds, there is no place which for some days of the year is not without the Sun, as was demonstrated in the third part. Rightly, then, are these zones named from cold, the torrid from the heat by which it is scorched. It remains, therefore, that the temperate zones are compared with the temperate parts of the year, because they are confined within the tropics and polar circles, nowhere having the Sun vertical, nowhere ever lacking the Sun for the whole natural day.
Recount the varieties of the solstices, and of heat and winter, through the seven positions of the sphere distinguished by the ecliptic, by which the five zones are distinguished and bounded. In the torrid zone the solstices nowhere give the Sun its highest altitude except at its boundaries. Since, therefore, the greatest altitude of the Sun at noon defines the beginning of summer, the least that of winter, summer here does not begin from either solstice except at the extremity of the zone, under the tropic; the other places of the torrid zone between, speaking by analogy, have two summers, the Sun passing through the zenith, and two winters, the Sun being at the solstices, when it turns aside as far as it can at the hours of noon from their zeniths to either side of the world. The remaining zones have a single summer and a single winter for each year, beginning the one from the high solstice, the other from the low. Under the equator, therefore, in the middle of the torrid zone, there are two summers at the two equinoxes, and two winters set between the summers at nearly equal intervals, at which times with us is the beginning of summer or winter: for on both sides the Sun turns aside from their zenith equally. Yet this variety is more like a perpetual temperateness than summer and winter. For the Sun does not fall on the zenith at the noon hours for many days, but passes quickly from the south into the north and conversely, since it spends the greatest part of the time in the arcs near the solstice. The days also, both summer and winter, being equal to their nights, have, with the due night interposed, a pleasant temperateness in the fervour of summer; their winters have the Sun, when it stands farthest off at the solstitial noon, still near the zenith and not removed more than 23½ degrees, while with us in our summer it is farther away. So the causes of their winter dispose more to heat than the causes of our summer.
Between the equator and the tropics, that is, on one side of the torrid zone, there are indeed two days of the year on which the Sun causes them the highest heat, passing through the zenith; but those two days, with the departure of the place from the equator, approach little by little both each other and the solstice: so that the one winter, or remission of heat, set between the two summers, is shorter than the opposite winter and so also hotter, because in it the Sun does not go so far from the zenith as in the other, and begins to have longer days, and with them longer heat, than not only in the other winter but even in the two summers themselves. And so in places near the tropic those two summers, surrounding the solstice, so far come together that they wholly crush out the other winter which the torrid zone can have at the higher solstice and turn it into a continuous summer. In sum, the torrid zone in a way feels a perpetual summer, in comparison with the other zones, and almost no winter, that is, no cold. It is tempered nevertheless, when it is most fervent, by perpetual rains and clouded sky, or by cold winds blowing from very high mountains, which in that zone are nevertheless covered with perpetual snow. This most grateful and effective refreshment is felt as soon as one has taken refuge under the shade of a tree in the open from the most violent rays of the Sun, as those testify who have gained for themselves the experience of many years in those places.
Under the tropic, on the borders of the torrid and temperate zones, a single summer first begins to be made at the high solstice itself and on the longest day: for then the Sun passes through the zenith for them; for the rest of the whole year, carried beyond the zenith, it declines toward the south. The heat here is most violent and far more intense than in the places toward the equator or under it: because the Sun then both sends its rays down from the zenith, and afflicts them continuously for many noons in order, with almost no change of declination perceived, and makes the days long and the nights short. Nay, in these ages the causes under the tropic of Cancer are more violent than under that of Capricorn, because the Sun by its proper motion seems to remain longer in the north than in the south.
Between the tropic and the polar circle, or in the temperate zone, places near the tropic differ nothing from those under the tropic itself. But the farther we have retired from the tropics, the more the noon Sun at the solstice also departs from the zenith, the less it burns in summer and the less it warms in winter, although, in some compensation for the lacking directness of the rays, it gives long days through the summer, and the farther the noon Sun is from the zenith at the solstice, the more prolonged are the days, but at the same time also the more violent the winters, the Sun raising itself but little and shining a few hours daily. Speaking summarily: the change of summer and winter is proper almost to the temperate zones alone, in comparison with the other zones.
Under the polar circle, which marks the borders of the temperate zone and the frigid zone, the true and consummate cause of cold and winter first shows itself, the Sun at the winter solstice not rising for one natural day, that is, not warming the earth at all. But as under the tropic there is still an almost continuous summer, and in place of winter only some slight remission of heat, so under the polar circle on the contrary there is an almost continuous winter, and in place of summer only some slight remission of cold, since the Sun, though shining for a continuous 24 hours, is never raised higher than 47 degrees, which altitude it has with us in April and September, and therefore the heating force is too feeble to dissolve in good time the snows and ice generated through the most savage winter. And as under the tropic the summer is more violent than in the middle of the torrid zone, so conversely under the polar circle the summer heat, such as it is, has less strength than in the middle of the frigid zone, because the Sun does not illuminate the snowy mountains from every side nor with continuous presence, as will now be clear.
Between the polar circle and the pole, or on the sides of the frigid zone, winter is almost continuous, and summer none, unless we wish to call the dissolution of the ice summer; in respect of which, the nearer the pole is approached, the lower indeed is the Sun at the noon hours of the solstitial days, but conversely the higher it remains at midnight in that part of the year when it does not set, and so, carried round about ice and snow and clods hardened with frost on every side, no space being allowed to the colds to gather themselves again by its absence, since it is never absent, it gathers some strength through the summer to dissolve the frost, less indeed near the polar circle, but more toward the pole itself. On the contrary the long duration of the winter cold is increased with the continuous night, to which, however, some alternation of days and nights still succeeds, and in the middle of them they enjoy the sight of the two equinoxes, apart from the summer solstice. But the winter solstice, or the observation of the Sun standing in its greatest southern declination, the long night and the icy horizon spread over the earth hide from them and snatch away. And of the summer solstice there are two proofs: one at noon, if the Sun no longer becomes higher than the day before; the other in the opposite part of the day, which answers to our midnight, if the Sun also then obtains an altitude nearly standing still, one which is found less before and after.
Under the pole, which is the middle of the frigid zone, there is again a single solstice, and that observable in the whole revolution of the Earth, with no distinction of noon or midnight. For the Sun is not higher for them at one hour than at another, nor do they distinguish the regions of the Earth, as we do, by the motion of the Sun and stars; all the vicissitude of our days and nights perishes among them, there is no knowledge of the equinoxes, none of the winter solstice; day is to them what summer is, night what winter is, each the length of half a year, the altitude of the Sun in the middle of their summer and day being as great as that of Italy in midwinter. When we have the equinox, that is, when the Sun remains visible to us for half the natural day, they behold half the body of the Sun: if, however, the refraction of the air does not disturb these reckonings. For it is consonant with what the Dutch observed in the frigid zone that it often happens that the Sun, though southern, in some certain region of the horizon (which they must needs mark only by mountains), or even in several regions, falls upon the fresh evaporations of the Earth, still transparent, not yet, that is, subdued by the cold, and through those refracted rays suddenly thrusts itself into view, and again, the Earth having turned and a drier region being presented, disappears. How much ice and snow is gathered through a whole half-year of the Sun’s absence, and how great the force of that winter, it is easy for anyone to estimate, and some of the Dutch have come upon the thing itself. And although these colds that encrust the Earth do not penetrate its inner parts, although the Earth within is warm by natural power, although the Sun present for the whole half-year and carried equally round the ice, licking it from every side, melting and consuming it, does indeed accomplish something toward driving away the winter, yet cold winds still remain, blowing from the surrounding places, nearer the solar track (where the force of the ice is greater), which hinder this summer work of the Sun not a little whenever they blow.
So that we may set up a kind of summary comparison: in the torrid zone summer rules, in the frigid zones winter, almost continuous, in the temperate there is a certain alternation of both, equable in the middle, and at the sides the property assigned to the neighbouring zone prevails.
What difference of shadows do astronomers observe between the zones? They call the inhabitants of the torrid zone amphiskioi, of the frigid zones periskioi, of the temperate heteroskioi: where the particle amphi has the same force as in the word amphitheatron. For in the torrid zone they have both shadows, that is, right and left, so named from the quarters toward which they are seen to move. This the poet Lucan means when he sings: Arabs, you have come into a world unknown to you, marvelling that the shadows of the groves go not to the left.
For Arabia Felix lies in the torrid zone, where the Sun throws shadows not only toward the north at the winter solstice, but also toward the south at the opposite solstice. Since, then, the shadow goes the way contrary to the Sun, the Sun, that is, advancing toward the west, the shadow tends to the east; therefore to one observing his own shadow the northern one will seem to go toward the right, exactly as with us, the southern toward the left, which we lack. For of the temperate zones each has only one or other shadow, the northern the right, the southern the left: they would more rightly be called heteroskioi. The inhabitants of the frigid zones are themselves also heteroskioi, but it pleased the authors to name them from a peculiar property periskioi, because their shadows, the Sun not setting, are carried all round through all the regions of the horizon.
What figures does the extremity of the shadow describe in each zone on the plane of the horizon? The matter is proper to gnomonics, and gave us in geometry the doctrine of conic sections. For a cone is to be imagined whose base is the circle of the natural day and whose vertex is at the extremity of the style, to which at the vertex there is another cone, which the plane of the horizon cuts; the section is traced by the moving extremity of the shadow. Therefore the path of the equinoctial shadow in all zones is a straight line, except under the pole, where the line of projection of the shadow is parallel to the horizon, and so does not fall upon it. The path of the other shadows, which they mark by their extremities, is a conic section: of which, since there are three kinds, the finite, such as the ellipse or circle, the infinite, such as the hyperbola or opposite sections, and between them the parabola, in some degree affecting finiteness though it too is infinite: in the frigid zones alone, then, can all these figures exist, so that the ellipse is proper to them, which under the pole itself is a perfect circle, or rather spirals, affecting the circle or ellipse, if you regard the joining of the several days on which the Sun does not set; for the plane of the horizon then cuts each side of the cone. But on that day on which the Sun grazes the horizon at natural midnight, about to set on the following days, the path of the shadow is a parabola, because the plane of the horizon is parallel to the upper side of the cone, since the declination of the Sun becomes equal to the altitude of the pole. And this parabola under the polar circle has place only on the single solstitial day: so that as the frigid zone is there terminated, so there also the ellipse and the parabola are terminated. But after day and night begin to succeed each other alternately, in the frigid as in the temperate and torrid zones, the figure of the path of the shadow is a hyperbola, or opposite sections, the common figure of the shadows of all the zones. For the plane of the horizon cuts the axis of the cones (the axis, that is, of the world) outside the vertices of the cones. By what difference the opposite sections stand in each zone is explained more particularly in works on gnomonics.
Where and when can the shadows of things erected perpendicularly become retrograde? In the torrid zone, when the declination of the same name is greater than the altitude of the pole: for then, with the Sun rising on this side of the equator, the shadow of a man is carried to the right from the winter setting toward the equinoctial setting, there lingering for some time as if standing still, and meanwhile, being made shorter, retraces its steps toward the left, that is, toward the winter setting, and the south, and the rising first winter, then equinoctial, where again stationary, the Sun being now about to set, it becomes retrograde a second time toward the right and the winter rising.
Is there also among us any usefulness of this exotic knowledge? It conduces to the construction of sciaterica composed of various planes, of which this one represents the horizon of the torrid zone, that one of the frigid zone, and so on.
Of the causes of the number and breadth of the zones.
That I may understand that so great a variety of the temperatures of the year and of days and nights, and of the zones which depends on it, exists from one single inclination of the axis about which the Earth rotates: say what would then be, if the axis of the Earth were not inclined? If that axis stood at right angles to the plane of the ecliptic, and the Earth so rotated about it as now, and at the same time were carried round the Sun as now, this right angle being constant: then the Sun indeed would be seen to go round in the annual space under the fixed stars and every day to rise and set, but there would be no distinction of the ecliptic into halves, quadrants or signs, no distinction of the year by the different qualities of heat and cold, all days equal to all nights, no distinction in the globe of the Earth except according to more and less. For since the axis of the Earth would so be set parallel to the axis of the ecliptic, the imaginary poles of the world would also coincide with the poles of the ecliptic. There would then be two points on the surface of the Earth at which the half body of the Sun would go round the horizon in eternal rotations, never raising itself, never sinking; from them, the nearer one came to the equator, the higher the Sun would become at noon, but always through the whole year at a constant altitude, until one came under the equator, where the Sun, in perennial alternation of days and nights, would always at noon pass beyond the zenith; so there the highest and single and perpetual summer would be, and under the poles the highest and single and perpetual winter. The Sun too in any place would so rise and set as some fixed star now does, always keeping to the same regions of the horizon. And so there would be some vicissitude on the Earth only by reason of day and night, none by reason of the year, for it would be just as if the Earth did not go round the Sun by its annual motion, save only that in other seasons of the year it would see other stars, as now also.
But what if the axis of the Earth lay wholly inclined in the very plane of the ecliptic, keeping a parallel position while the Earth is carried about the Sun? Then there would indeed be vicissitudes, not only of days and nights by the revolution of the Earth about its axis, but also of the seasons of the year by the circumlation of the Earth, but they would be disproportionate vicissitudes, and in a way all common to all the places of the earth. For the poles of the ecliptic would appear to revolve in the equator, the poles of the world would be in the ecliptic, namely at the beginning of Cancer and Capricorn; the Sun would therefore come in summer to the upper pole of the world, in winter to the lower: there it would make for those who live under the pole a day of the length of one half-year, and in the middle of it would scorch them most violently, since at right angles, as now in the torrid zone, and at the same time not setting, as now on the long day of the frigid zone, and moreover not changing place. In winter on the contrary those under the pole would be numb as now, but would have pure and deepest night, diluted by no twilight, as now; so through summer they would be destroyed by flames and squalor, through winter by frost and darkness: extreme contraries would fall upon one place.
Conversely, to those who live under the equator the Sun would pass through the zenith at the equinoctial points, as now, at the solstitial points would sink down to the horizon, and there in one place of the horizon be turned as in a lathe, showing now one, now another particle of its body to be seen.
So to all the places intermediate between the poles and the equator all the properties of all the zones would belong. For they would have the Sun vertical in two summers in the year, and continuous days in one of their winters, and continuous nights in the other of their winters. Those nearer the pole would have both a continuous day and a continuously vertical Sun at the same time, and that for no short time.
Say also what would then happen if, with any constant inclination of the axis of the Earth posited, the position of the axis did not remain parallel in the circumlation of the Earth, but looked perpetually toward the Sun itself? What would result, a right angle of inclination being posited, was said at the beginning; there would be no vicissitude. The same would follow if the axis, projected into the plane of the ecliptic, remained perpetually turned straight toward the Sun, except that in the former case the poles of the world coincide with the poles of the ecliptic, in the latter they would go round in the ecliptic itself with the annual motion, and what follows from this. But with the axis posited as inclined, so that the axis keeps a constant oblique angle with the line which connects the centres of the Sun and the Earth, in a plane however at right angles to the plane of the ecliptic, whatever variety and vicissitude arises at the position of each angle of inclination, there would now be no vicissitude through the whole year, but it would affect the different places of the Earth with so much the greater diversity as it was more oblique, so that the places which the Sun now leaves once in a year would then be deprived of the sight of the Sun forever, those which have the Sun once in a year not setting would then enjoy that continual sight, and not under the equator, but under the tropic, or (if the axis were laid wholly down in the plane of the ecliptic, extended toward the Sun) under the very pole of the world they would always have the Sun vertical. The fixed stars would seem to measure the whole zodiac in the annual space, the pole of the Earth completing its annual circuit either under the ecliptic itself or under another parallel. So the fixed stars, which have the account of place, would be accounted not fixed, the Sun, which is placed, fixed, though in the opposite parts of the year it would travel contrary ways in the diurnal motion; great would be the confusion of the motions, very difficult the comprehension.
Nor would anything else follow if the angle between the axis of the Earth and the line connecting the centres were in a plane oblique to the ecliptic: except that then the Sun would be seen to move not under the tropic circle drawn through the beginnings of Cancer or Capricorn, but under some interior one and (the axis then lying down in the plane) again in a tropic wandering in breadth. Everywhere there is lacking either the vicissitude of the seasons of the year, or the distinction of the zones adapted to the vicissitudes, or both.
Since, then, the right angle of the axis with the plane of the ecliptic was rejected, lest there should be no vicissitude, and total inclination, or the mere projection of the axis into the plane of the ecliptic, was rejected, lest it be excessive: why was not a mean angle between 90 and 0 chosen, namely 45°, half a right angle? If that angle were half a right angle, there would be only three zones, one torrid, two frigid, and where the Sun ceases in summer to become vertical, there it would cease at the winter solstice to rise. The contrary qualities of summer and winter would so have the globe of the Earth distributed between them that no middle and temperate region would intervene; whereas elsewhere these qualities naturally admit a mean.
Whence, then, do you think the magnitude of the angle at which the axis of the Earth is inclined, or what is the same, of the declination of the ecliptic, was taken by the all-wise Creator? Indeed I pray with a chaste mind that, by his favouring divinity, by his favour, by his spirit dictating, we may be able to discourse of the secrets of his counsels, and I judge it right, nay lawful, to inquire modestly into the numbers, measures and weights by which rules he himself made all things, because he himself made the knowledge of these things common to man with himself, and in that matter set no smallest particle of his image in man, approving what he had made as very good, and to approve it much more if by the light of this image we also bring into the light of knowledge the use of numbers, weights and measures which he himself showed in creating. For these are not secrets such that investigation of them is forbidden to us, but they are set before us in place of a mirror, that by their explanation we may in some measure behold the goodness and wisdom of the Creator.
But since there are two chief kinds of causes which the Creator, best and greatest, is found everywhere to have followed: the formal, or the beauty of the archetype, and the final, or the usefulness of living creatures: I therefore judge that if the Creator in this conformation had regarded the beauty of demonstrable figures, he would not have chosen the fifteen-sided figure, whose side cuts off from the circle 24°, as great an obliquity of the ecliptic as the Indians observed, and Eratosthenes a little less, namely 23° 51½′. For although the fifteen-sided figure is demonstrable, its demonstration nevertheless holds a remote degree from equality and is in a way accidental to the fifteen-sided figure as such, and belongs rather to the triangle and the pentagon, by the force and properties of which figures this demonstration is carried out; see the figure above on page 202. Indeed this somewhat extraneous demonstration is of no use to the fifteen-sided figure for the composition of a regular body, while the other demonstrable figures help this composition in various ways. The beauty of figures, therefore, has another place, and particularly in the conformation of the celestial orbs; in the distribution of the zones the use of the living creatures that were to inhabit them had to come first. But of that use it has already been said that there had to be some variety and vicissitude. For since the Sun has heat, the Earth cold, from the nature of matter, and the Earth is an opaque and round body, the Sun certainly, unless motion intervened, could not warm the whole of it from every side, and therefore the daily revolution of the Earth about its axis seems to have been decreed, as was disputed above in the first book. Again, because the Earth was to be the dwelling place of things to be generated and corrupted, it was not fitting that the single parts of the Earth should be affected equally at every time by the Sun, each according to its own measure. So, because by simple revolution, the axis being at right angles to the plane of the ecliptic, the poles and the places near the poles seem to be deserted by heat, the axis had to be inclined, that those parts might be turned alternately toward the Sun. Finally, by simple revolution and a right axis, as was said above, cold would be seen in at least two points, heat in a single line only, which has no breadth: the whole surface of the sphere would have had confused limits of heat and cold without manifest distinction. But it pleased the Creator to distinguish, as light from darkness, so also the limits and regions and tracts of light and shade, of heat and cold. For these causes the axis had to be inclined.
Third, since even the simple rotation of the Earth, the axis being at right angles to the plane of the ecliptic, would set certain bounds to cold under the two poles and to heat under the equator, the tracts of the frigid zones had therefore to be set about the poles and of the torrid about the equator: two frigid, on account of the two poles, one torrid.
Fourth, since it would not be good that extremes should be joined without a mean, two temperate zones had therefore to intervene.
Fifth, to these considerations drawn from use the regard to beauty now puts the crown. For nothing in geometry is more beautiful than equality, if nothing stand in its way. It is therefore not unlike the truth that the Creator ordained from the beginning the breadths of the five zones equal. And since the meridian drawn through the poles cuts the torrid and temperate zones at opposite places, there result six portions of the meridian, to which are added the single sections of the single frigid zones, and the portions are eight in number. In the figure: CE, EI, IM, MN, NR, RS, ST, TC.
From these elements, then, and not from any regard to beauty in the eight-sided figure itself, nor its inscription in the meridian, I think the eightfold division of the terrestrial meridian was established; so that the common breadth of all the zones would be 45°, of German miles 675, and the declination of the ecliptic 22° 30′.
You seem to hand down a breadth of the zones foreign to the truth. Indeed the breadth of the torrid zone is double the obliquity of the ecliptic, namely 47° 3′, 706 miles today; so great, then, is also the breadth of the two frigid zones, and there remains for the temperate zones a breadth of 42° 57′, 644 miles, because the declination of the ecliptic is 23° 31½′ today. But as it was found greater of old, namely 23° 51½′, so also before those times it could have been less, and at the creation of the world 22° 30′, and thence grown by a degree and a half. So let this speculation be left to our posterity to be further tested.
Does no other equality appear here than that alone of the parts of the meridian, or the breadth of the zones? Nay, this also is to be considered, that if the obliquity of the ecliptic were 24° 17′ 42″, that is, as much greater than it was in the time of Eratosthenes as it is now less than it was of old, which is not absurd to suppose it once to have been: then the surface of the torrid zone, together with the surfaces of the two frigid zones, would have exactly as great an area as the two temperate have; so the surface of the Earth would be most equally distributed between the extremes and the temperate. And if the declination were 23° 35′, as much as Albategnius found 730 years ago, then the torrid zone would be to one of the temperate as 4 to 3.
What is the proportion of the surfaces to each other today? Today the spaces of the zones stand thus.
Of such parts as the whole surface is worth 100000, the torrid is worth 39915, a temperate 25887, a frigid 4156; temperate and frigid together 30043; the two frigid 8311; the torrid with the 2 frigid 48226; but the two temperate 51774.
Since, then, whatever belongs to the temperate surface lies open in a space of four hundred and eighty hundreds of thousands of square German miles, let us give half to the waters (for as the northern temperate zone is for the most part spread with lands, so the southern is covered with the waters of the ocean); there will remain two hundred and forty hundreds of thousands, and besides that eighteen thousand square miles of temperate and habitable earth: of which part of the surface the two hundred and forty thousandth part has a hundred square miles, ten that is in length, ten in breadth, about as much as Upper Austria extends. And how ridiculous is he who in any census sets down this to be measured: for of the whole surface of the Earth the portion is not much greater than the millionth.